You start with 100 dollars. When you flip a coin and receive a head, you gain 100 dollars. If you flip the coin and received a tail, you lose half of your current money. What is the expected amount of money you will have after 4 flips?
I know that if you gained 100 dollars on heads and lost 50 dollars on tails you could say: E(final money) = (100 * 0.5) - (50 * 0.5).
I also know that if you doubled your money on heads and halved your money on tails then E(final money) = 100 * 2^(# of heads) * (1/2)^(#of tails)
However, this problem seems to be mixing both addition and multiplication, so I am unsure of how to combine them into a single equation to receive a solution.